Mangakis was born on June 25, 1922, in Athens. He was the son of Antonios Mangakis - a Member of the Hellenic Parliament from the Cyclades - and Angeliki Mangaki - the daughter of former Prime Minister Stylianos Gonatas.
Mangakis studied Law in Athens. After serving in the Hellenic Navy, he completed his post-graduate studies at the University of Munich where, in 1953, he was appointed a lecturer. In 1955 he was appointed at the Law School of the University of Athens.
In addition to his career as a professor, Mangakis practised law, defending many students and workers during the years of the "uncompromising struggle" protests against the Constantine Karamanlis' government's undemocratic policies.
In February 1969, the Junta that had seized power two years earlier, dismissed him from his post at the University of Athens Law School. In July of that same year, Mangakis was arrested for his anti-Junta activities. In a trial in 1970, he was given an 18-year jail sentence. While imprisoned, Mangakis wrote articles, critical of the government, that were published abroad as well as locally by the underground press.
Mangakis was released in 1972 by reason of declining health. He left for Germany where he lectured at the University of Heidelberg whilst continuing his pro-democracy efforts.
In July 1974 the Junta collapsed in the aftermath of the Turkish invasion of Cyprus. Mangakis returned to Greece and took part in the unity government of Constantine Karamanlis as Minister of Public Works. Later that year, he was elected to Parliament under the banner of the Centre Union party.